The top Dem on House Armed Services said he was "skeptical" the measure would pass.
The White House request has faced criticism from the GOP and Dems.
Ashton Carter, 60, will be the 25th secretary of Defense and Obama's fourth.
It is unclear if the language will pass muster with Dems.
Prominent veterans groups did not call for the "NBC Nightly News" host to resign.
Ashton Carter heads for his confirmation hearing before the Armed Services panel.
A bloc of Senate Democrats have said they won't support a floor vote until late May.
"She said ... I’ll do it, period,” Rep. Elijah Cummings (Md.) said.
Hagel said the unrest would be "factored in" to decisions on releasing detainees.
Obama will deliver his penultimate State of the Union address.
A top U.S. commander in Iraq said the terror groups is switching to "defense."
The bill will level new sanctions on Russia and pave the way for lethal arms to Ukraine.
The head of anti-ISIS coalition wouldn't define the key language.
Lawmakers from both parties have panned Obama's request for authorization of force.
Obama's war powers request was met with skepticism from both parties.
Pressure is building on Obama to bolster aid to Kiev.
Carter smoothly navigated tough questions and is expected to be confirmed.
The $585 billion request would break defense budget caps.
The hearing came days before the administration releases its 2016 Defense budget request.
Senators introduced a bill in support of allowing talks to conclude before sanctions legislation.
The administration is objecting to an up-or-down vote in Congress on a deal.
Tuesday's SOTU wil be the first since the U.S. stepped up the fight against ISIS.
Fifteen aircraft conducted 45 strikes in northwestern Iraq earlier this month.
Sens.-elect Tom Cotton (Ark.) and Joni Ernst (Iowa) are joining the panel.